First, this study obtained the fields of an Airy beam (AiB) with optical vortex (OV) for a Fourier transform (FT) system and a fractional Fourier transform (fractional FT) system; thereafter, their intensity and phase patterns were simulated numerically. The splitting on each line of the phase pattern indicates the position of an OV. The results show that the OV position will change when the power of the fractional FT (p) changes. Moreover, the uniformity of the spot beam disappears for the beam with OV. Further, the characteristics of an AiB such as number, width, height, uniformity of the spot beam and the effective beam size will change when there is a change in the values of p and z.
